7x-8/(x+1)=x

Solution for 7x-8/(x+1)=x equation:

7x-8/(x+1)=x

We move all terms to the left:

7x-8/(x+1)-(x)=0


Domain of the equation: (x+1)!=0

We move all terms containing x to the left, all other terms to the right

x!=-1

x∈R


We add all the numbers together, and all the variables

6x-8/(x+1)=0

We multiply all the terms by the denominator


6x*(x+1)-8=0

We multiply parentheses

6x^2+6x-8=0

a = 6; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·6·(-8)
Δ = 228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{57}}{2*6}=\frac{-6-2\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{57}}{2*6}=\frac{-6+2\sqrt{57}}{12}
$